How to apply object rotation on a delta position vector?

I have a motion delta (from VR headset → previous location - current location), and I’d like to apply it to an object. If I just add them together they look funny(directions get mixed up), so I guess I have to apply the rotation of the Actor as well. What is the formula for applying that rotation to my motion delta?

Found this on stackoverflow, but it’s only 2d.

angle = dir * pi / 3    
newx = x + amount * sin(angle)    
newy = y + amount * cos(angle)